Hydrothermal coupling in a self-affine rough fracture

The influence of the multiscale fracture roughness on the heat exchange when a cold fluid enters a fractured hot solid is studied numerically on the basis of the Stokes equation and in the limit of both hydrolubrication and thermolubrication. The geometrical complexity of the fracture aperture is modeled by small self-affine perturbations added to a uniform aperture field. Thermal and hydraulic properties are characterized via the definition of hydraulic and thermal apertures both at microscopic and macroscopic scales and obtained by comparing the fluxes to the ones of flat fractures. Statistics over a large number of fracture configurations provide an estimate of the average behavior and its variability. We show that the long-range correlations of the fracture roughness induces strong channeling effects that significantly influence the hydraulic and thermal properties. An important parameter is the aspect ratio (length over width) of the fracture: we show, for example, that a downstream elongated rough fracture is more likely to inhibit the hydraulic flow and subsequently to enhance the thermal exchange. Fracture roughness might, in the opposite configuration, favor strong channeling which inhibits heating of the fluid. The thermal behavior is in general shown to be mainly dependent on the hydraulic one, which is expressed through a simple law.